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This paper aims to correct the existing mixed integer programming (MIP) model proposed by Yadav et al. (2019) [“Bi-objective optimization for sustainable supply chain network design in omnichannel.”, Journal of Manufacturing Technology Management, Vol. 30 No. 6, pp. 972–986].

This paper first presents a counterexample to show that the existing MIP model is incorrect and then proposes an improved mixed integer linear programming (MILP) model for the considered problem. Last, a numerical experiment is conducted to test our improved MILP model.

This paper demonstrates that the formulations of the facility capacity constraints and the product flow balance constraints in the existing MIP model are incorrect and incomplete. Due to this reason, infeasible solutions could be identified as feasible ones by the existing MIP model. Hence, the optimal solution obtained with the existing MIP model could be infeasible. A counter-example is used to verify our observations. Computational results verify the effectiveness of our improved MILP model.

This paper gives a complete and correct formulation of the facility capacity constraints and the product flow balance constraints, and conducts other improvements on the existing MIP model. The improved MILP model can be easily implemented and would help companies to have more effective distribution networks under the omnichannel environment.

The ocean transportation of automobiles is carried out by specialized Roll‐on/Roll‐off ships, which are designed to carry a large number of automobiles at a time. Many of these shipping companies have vertically integrated or collaborated with other logistics services providers to offer integrated maritime logistics solution to car manufacturers. The purpose of this study is to develop an optimization model to address the tactical level maritime logistics planning for such a company.

The problem is formulated as a mixed integer linear program and we propose an iterative combined Ant colony and linear programming‐based solution technique for the same.

This paper can integrate the maritime transportation planning of internally managed cargoes with the inventory management at the loading and discharging ports to minimize supply‐chain cost and also maximize additional revenue through optional cargoes using same fleet of ships.

The mathematical model does not consider the variability in production and consumption of products across various locations, travel times between different nodes, etc.

The suggested mathematical model to the supply‐chain planning problem and solution technique can be considered in the development of decision support system for operations planning.

This paper extends the maritime inventory routing model by considering simultaneous planning of optional cargoes with internally managed cargoes.

This paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon.

A general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models.

Results show that both approaches are relevant for solving the energy management problem of the building MG.

Introduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. Linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.

This paper aims to address the problem of optimal allocation of demand of items among candidate suppliers to maximize the purchase value of items. The purchase value of the items directly relates to cost and quality of raw materials purchased from the supplier. In an increasingly competitive environment, firms are paying more attention to selecting the right suppliers for procurement of raw materials and component parts for their products. The present research work focuses on this issue of supply chain management.

This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches.

The supply chain network is witnessing a changing business environment due to government policies aimed at promoting new small manufacturing enterprises (small and medium-sized enterprises) for intermediate parts and components. Hence, the managers have an option to select a new group of suppliers and allocate the optimal multi-period demand among the new group of suppliers to maximize their purchase value. In this context, the proposed hybrid model would be beneficial for the managers to operate their supply chain effectively and efficiently. The present research work will be helpful for the managers who are interested to reconfigure their supply chain under the failure of any supply chain partner or in a changing business environment. The model provides flexibility to the managers for evaluation of the different available alternatives to take a decision of optimal demand allocation among the suppliers. The proposed hybrid (fuzzy, TOPSIS and MILP) model provides more objective information for supplier evaluation and demand allocation among suppliers in a supply chain. The managers can use the proposed model to the analysis of other management decision-making problems.

This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. This hybrid algorithm prioritizes the suppliers and then allocates the multi-period demand among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches.

A circular economy (CE) is an economic system that tries to eliminate waste and continually use resources. Due to growing environmental concerns, supply chain (SC) design should be based on the CE considerations. In addition, responding and satisfying customers are the challenges managers constantly encounter. This study aims to improve the design of an agile closed-loop supply chain (CLSC) from the CE point of view.

In this research, a new multi-stage, multi-product and multi-period design of a CLSC network under uncertainty is proposed that aligns with the goals of CE and SC participants. Recycling of goods is an important part of the CLSC. Therefore, a multi-objective mixed-integer linear programming model (MILP) is proposed to formulate the problem. Besides, a robust counterpart of multi-objective MILP is offered based on robust optimization to cope with the uncertainty of parameters. Finally, the proposed model is solved using the e-constraint method.

The proposed model aims to provide the strategic choice of economic order to the suppliers and third-party logistic companies. The present study, which is carried out using a numerical example and sensitivity analysis, provides a robust model and solution methodology that are effective and applicable in CE-related problems.

This study shows how all upstream and downstream units of the SC network must work integrated to meet customer needs considering the CE context.

The main goal of the CE is to optimize resources, reduce the use of raw materials, and revitalize waste by recycling. In this study, a comprehensive model that can consider both SC design and CE necessities is developed that considers all SC participants.

This paper designs an optimal closed-loop supply chain network with an integrated forward and reverse logistics to examine the possibility of remanufacturing end-of-life (EoL) ships.

Explanatory variables are used to estimate the number of EoL ships available in a closed-loop supply chain network. The estimated number of EoL ships is used as an input in the model and then it is solved by a mixed-integer linear programming (MILP) model of the closed-loop supply chain network to minimise the total logistic costs. A discounted payback period formula is developed to calculate the length of time to recoup an investment based on the investment's discounted cash flows. Existing ship wrecking industry clusters in the Western region of India are used as the case study to apply the proposed model.

The MILP model has optimised the total logistics costs of the closed-loop supply network and ascertained the optimal number and location of remanufacturing for building EoL ships. The capital and variable costs required for establishing and operating remanufacturing centres are computed. To remanufacture 30 ships a year, the discounted payback period of this project is estimated to be less than two years.

Ship manufacturing businesses are yet to re-manufacture EoL ships, given high upfront capital expenditure and operational challenges. This study provides management insights into the costs and benefits of EoL ship remanufacturing; thus, informing the decision-makers to make strategic operational decisions.

The design of an optimal close loop supply chain network coupled with a Bayesian network approach and discounted payback period formula for the collection and remanufacturing of EoL ships provides a new integrated perspective to ship manufacturing.

To maximize the network total profit by calculating the difference between costs and revenue (first objective function). To maximize the positive impact on the environment by integrating GSCM factors in RL (second objective function). To calculate the efficiency of disassembly centers by SDEA method, which are selected as suppliers and maximize the total efficiency (third objective function). To evaluate the resources and total efficiency of the proposed model to facilitate the allocation resource process, to increase resource efficiency and to improve the efficiency of disassembly centers by Inverse DEA.

The design of a closed-loop logistics network for after-sales service for mobile phones and digital cameras has been developed by the mixed-integer linear programming method (MILP). Development of MILP method has been performed by simultaneously considering three main objectives including: total network profit, green supply chain factors (environmental sustainability) and maximizing the efficiency of disassembly centers. The proposed model of study is a six-level, multi-objective, single-period and multi-product that focuses on electrical waste. The efficiency of product return centers is calculated by SDEA method and the most efficient centers are selected.

The results of using the model in a case mining showed that, due to the use of green factors in network design, environmental pollution and undesirable disposal of some electronic waste were reduced. Also, with the reduction of waste disposal, valuable materials entered the market cycle and the network profit increased.

(1) Design a closed-loop reverse logistics network for after-sales services; (2) Introduce a multi-objective multi-echelon mixed integer linear programming model; (3) Sensitivity analysis use Inverse-DEA method to increase the efficiency of inefficient units; (4) Use the GSC factors and DEA method in reverse logistics network.

This study aims to reduce carbon emissions and costs in an automobile production plant by improving the operational management efficiency of a serial assembly line assisted by a feeding electric tow vehicle (ETV).

A multi-objective function is formulated to minimize the energy consumption of the ETV from which emissions and costs are measured. First, a mixed-integer linear programming model is used to solve the feeding problem for different sizes of the assembly line. Second, a bi-objective optimization (HBOO) model is used to simultaneously minimize the most eco-efficient objectives: the number of completed runs (tours) by the ETV along the assembly line, and the number of visits (stops) made by the ETV to deliver kits of components to workstations.

The most eco-efficient strategy is always the bi-objective optimal solution regardless of the size of the assembly line, whereas, for single objectives, the optimization strategy differs depending on the size of the assembly line.

Instances of the problem are randomly generated to reproduce real conditions of a particular automotive factory according to a previous case study. The optimization procedure allows managers to assess real scenarios improving the assembly line eco-efficiency. These results promote the implementation of automated control of feeding processes in green manufacturing.

The HBOO-model assesses the assembly line performance with a view to reducing the environmental impact effectively and contributes to reducing the existent gap in the literature. The optimization results define key strategies for manufacturing industries eager to integrate battery-operated motors or to address inefficient traffic of automated transport to curb the carbon footprint.

The purpose of this paper is to provide feasible and fast solutions for the multi-objective airport gate assignment problem (AGAP) considering both passenger-oriented and airline-oriented objectives, which is the total walking distance from gate to baggage carousels (TWD) and the total aircraft fuel consumption during taxi operations (TFC). In addition, obtaining feasible and near-optimal solutions in a short time reduces the gate planning time to be spent by air traffic controllers.

The mixed integer linear programming (MILP) approach is implemented to solve the multi-objective AGAP. The weighted sum approach technique was applied in the model to obtain non-dominated solutions. Because of the complexity of the problem, the simulated annealing (SA) algorithm was used for the proposed model. The results were compared with baseline results, which were obtained from the algorithm using the fastest gate assignment and baggage carousel combinations without any conflict taking place at the gate assignments.

The proposed model noticeably decreased both the TWD and TFC. The improvement of the TWD and TFC changed from 22.8% to 46.9% and from 4.7% to 7.1%, respectively, according to the priorities of the objectives. Additionally, the average number of non-dominated solutions was calculated as 6.94, which presents many feasible solutions for air traffic controllers to manage ground traffic while taking the airline and passenger objectives into consideration.

The proposed MILP model includes the objectives of different stakeholders: air traffic controllers, passengers and airlines. In addition, the proposed model can provide feasible gate and baggage carousel assignments together in a short time. Therefore, the model creates a flexibility for air traffic controllers to re-arrange assignments if any unexpected situations take place.

The proposed MILP model combines the TWD and TFC together for the AGAP problem using the SA. Moreover, the proposed model integrates passenger-oriented and airline-oriented objectives together and reveals the relationships between the objectives in only a short time.

The purpose of this paper is to design and optimize economic and environmental dimensions in a sustainable supply chain (SSC) network. This paper developed a mixed-integer linear programing (MILP) model to incorporate economical and environmental data for multi-objective optimization of the SSC network.

The overall objective of the present study is to use high-quality raw materials, at the same time the lowest amount of pollution emission and the highest profitability is achieved. The model in the problem is solved using two algorithms, namely, multi-objective genetic and multi-objective particle swarm. In this research, to integrate sustainable supplier selection and optimization of sustainability performance indicators in supply chain network design considering minimization of cost and time and maximization of sustainability indexes of the system.

The differences found between the genetic algorithms (GAs) and the MILP approaches can be explained by handling the constraints and their various logics. The solutions are contrasted with the original crisp model based on either MILP or GA, offering more robustness to the proposed approach.

The model is applied to Mega Motor company to optimize the sustainability performance of the supply chain i.e. economic (cost), social (time) and environmental (pollution of raw material). The research method has two approaches, namely, applied and mathematical modeling.

There is limited research designing and optimizing the SSC network. This study is among the first to integrate sustainable supplier selection and optimization of sustainability performance indicators in supply chain network design considering minimization of cost and time and maximization of sustainability indexes of the system.